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The field of nuclear astrophysics is devoted to the study of the creation of the chemical elements. By nature, it is deeply intertwined with the physics of the Sun. The nuclear reactions of the proton-proton cycle of hydrogen burning, including the 3He({\alpha},{\gamma})7Be reaction, provide the necessary nuclear energy to prevent the gravitational collapse of the Sun and give rise to the by now well-studied pp, 7Be, and 8B solar neutrinos. The not yet measured flux of 13N, 15O, and 17F neutrinos from the carbon-nitrogen-oxygen cycle is affected in rate by the 14N(p,{\gamma})15O reaction and in emission profile by the 12C(p,{\gamma})13N reaction. The nucleosynthetic output of the subsequent phase in stellar evolution, helium burning, is controlled by the 12C({\alpha},{\gamma})16O reaction. In order to properly interpret the existing and upcoming solar neutrino data, precise nuclear physics information is needed. For nuclear reactions between light, stable nuclei, the best available technique are experiments with small ion accelerators in underground, low-background settings. The pioneering work in this regard has been done by the LUNA collaboration at Gran Sasso/Italy, using a 0.4 MV accelerator. The present contribution reports on a higher-energy, 5.0 MV, underground accelerator in the Felsenkeller underground site in Dresden/Germany. Results from {\gamma}-ray, neutron, and muon background measurements in the Felsenkeller underground site in Dresden, Germany, show that the background conditions are satisfactory for nuclear astrophysics purposes. The accelerator is in the commissioning phase and will provide intense, up to 50{\mu}A, beams of 1H+, 4He+ , and 12C+ ions, enabling research on astrophysically relevant nuclear reactions with unprecedented sensitivity., Comment: Submitted to the Proceedings of the 5th International Solar Neutrino Conference, Dresden/Germany, 11-14 June 2018, to appear on World Scientific -- updated version (Figure 2 and relevant discussion updated, co-author A. Domula added)

We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (ii) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ-OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness (ACR), as we demonstrate for the EnvZ-OmpR pathway., Comment: 23 pages, 0 figures

An embedding $\varphi \colon (M_1, \omega_1) \to (M_2, \omega_2)$ (of symplectic manifolds of the same dimension) is called $\epsilon$-symplectic if the difference $\varphi^* \omega_2 - \omega_1$ is $\epsilon$-small with respect to a fixed Riemannian metric on $M_1$. We prove that if a sequence of $\epsilon$-symplectic embeddings converges uniformly (on compact subsets) to another embedding, then the limit is $E$-symplectic, where the number $E$ depends only on $\epsilon$ and $E (\epsilon) \to 0$ as $\epsilon \to 0$. This generalizes $C^0$-rigidity of symplectic embeddings, and answers a question in topological quantum computing by Michael Freedman. As in the symplectic case, this rigidity theorem can be deduced from the existence and properties of symplectic capacities. An $\epsilon$-symplectic embedding preserves capacity up to an $\epsilon$-small error, and linear $\epsilon$-symplectic maps can be characterized by the property that they preserve the symplectic spectrum of ellipsoids (centered at the origin) up to an error that is $\epsilon$-small. We sketch an alternative proof using the shape invariant, which gives rise to an analogous characterization and rigidity theorem for $\epsilon$-contact embeddings., Comment: 17 pages

We start from a parametrized system of $d$ generalized polynomial equations (with real exponents) for $d$ positive variables, involving $n$ generalized monomials with $n$ positive parameters. Existence and uniqueness of a solution for all parameters and for all right-hand sides is equivalent to the bijectivity of (every element of) a family of generalized polynomial/exponential maps. We characterize the bijectivity of the family of exponential maps in terms of two linear subspaces arising from the coefficient and exponent matrices, respectively. In particular, we obtain conditions in terms of sign vectors of the two subspaces and a nondegeneracy condition involving the exponent subspace itself. Thereby, all criteria can be checked effectively. Moreover, we characterize when the existence of a unique solution is robust with respect to small perturbations of the exponents or/and the coefficients. In particular, we obtain conditions in terms of sign vectors of the linear subspaces or, alternatively, in terms of maximal minors of the coefficient and exponent matrices. Finally, we present applications to chemical reaction networks with (generalized) mass-action kinetics.

We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the square and the edges and corners of the cube. The main idea is to transfer estimates for the continuous bilaplacian using a new discrete compactness argument and a discrete version of the Cacciopoli (or reverse Poincar\'e) inequality. One application that we have in mind is the study of entropic repulsion for the membrane model from statistical physics.

The discovery of ferroelectric properties of binary oxides revitalized the interest in ferroelectrics and bridged the scaling gap between the state-of-the-art semiconductor technology and ferroelectric memories. However, before hitting the markets, the origin of ferroelectricity and in-depth studies of device characteristics are needed. Establishing a correlation between the performance of the device and underlying physical mechanisms is the first step toward understanding the device and engineering guidelines for a novel, superior device. Therefore, in this paper a holistic modeling approaches which lead to a better understanding of ferroelectric memories based on hafnium and zirconium oxide is addressed. Starting from describing the stabilization of the ferroelectric phase within the binary oxides via physical modeling the physical mechanisms of the ferroelectric devices are reviewed. Besides, limitations and modeling of the multilevel operation and switching kinetics of ultimately scaled devices as well as the necessity for Landau-Khalatnikov approach are discussed. Furthermore, a device-level model of ferroelectric memory devices that can be used to study the array implementation and their operational schemes are addressed. Finally, a circuit model of the ferroelectric memory device is presented and potential further applications of ferroelectric devices are outlined.

We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of ap- proximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs., Comment: Result now covers the two well problem in full generality. Proof simplified. New Figure 9 illustrates geometry of separation

S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles., Comment: 26 pages, 5 figures

The purpose of this paper is to carry out a classical construction of a non-constant holomorphic disk with boundary on (the suspension of) a Lagrangian submanifold in $\mathbb{R}^{2 n}$ in the case the Lagrangian is the lift of a coisotropic (a.k.a. pre-Lagrangian) submanifold in (a subset $U$ of) $\mathbb{R}^{2 n - 1}$. We show that the positive lower and finite upper bounds for the area of such a disk (which are due to M. Gromov and J.-C. Sikorav and F. Laudenbach-Sikorav for general Lagrangians) depend on the coisotropic submanifold only but not on its lift to the symplectization. The main application is to a $C^0$-characterization of contact embeddings in terms of coisotropic embeddings in another paper by the present author. Moreover, we prove a version of Gromov's non-existence of exact Lagrangian embeddings into standard $\mathbb{R}^{2 n}$ for coisotropic embeddings into $S^1 \times \mathbb{R}^{2 n}$. This allows us to distinguish different contact structures on the latter by means of the (modified) contact shape invariant. As in the general Lagrangian case, all of the existence results are based on Gromov's theory of $J$-holomorphic curves and his compactness theorem (or persistence principle). Analytical difficulties arise mainly at the ends of the cone $\mathbb{R}_+ \times U$., Comment: 13 pages; v2: fixed technical issue regarding the function Lambda in (the old) subsection 4.2; most changes in (new) subsections 4.2 and 4.3 (up to end of proof of lemma), and minor cosmetic changes and typos corrected throughout; none of results affected by update

Oxygen-deficient TiO$_2$ in the rutile structure as well as the Ti$_3$O$_5$ Magn{\'e}li phase is investigated within the charge self-consistent combination of density functional theory (DFT) with dynamical mean-field theory (DMFT). It is shown that an isolated oxygen vacancy (V$_{\rm O}$) in titanium dioxide is not sufficient to metallize the system at low temperatures. In a semiconducting phase, an in-gap state is identified at $\varepsilon_{\rm IG}^{\hfill}\sim -0.75\,$eV\, in excellent agreement with experimental data. Band-like impurity levels, resulting from a threefold V$_{\rm O}$-Ti coordination as well as entangled $(t_{2g},e_g)$ states, become localized due to site-dependent electronic correlations. Charge localization and strong orbital polarization occur in the V$_{\rm O}$-near Ti ions, which details can be modified by a variation of the correlated subspace. At higher oxygen vacancy concentration, a correlated metal is stabilized in the Magn{\'e}li phase. A V$_{\rm O}$-defect rutile structure of identical stoichiometry shows key differences in the orbital-resolved character and the spectral properties. Charge disproportionation is vital in the oxygen-deficient compounds, but obvious metal-insulator transitions driven or sustained by charge order are not identified., Comment: 11 pages, 11 figures

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions and the resulting planar ODE. We characterize the parameters (positive coefficients and real exponents) for which the unique positive equilibrium is a center.

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and stability of the positive equilibrium, in particular, we characterize its global asymptotic stability in terms of the kinetic orders., Comment: 28 pages, 9 figures